What does this research mean for the field?

The full class group of a number field is exactly the group of affine descent obstructions for the capitulated affine system over the Hilbert class field, and an invariant generator exists if and only if the prime is principal. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To establish Galois descent theorems for capitulated affine Bost-Connes boundary systems and characterize how ideal class groups emerge as descent obstructions.

September 8, 2026Open Access

Galois descent for affine Bost-Connes boundaries: capitulation, the obstruction cocycle, and the emergence of the class group

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Authors

RCRuqing ChenZhejiang Normal University

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Implication

Theoretical analysis uncovers affine descent obstructions in number field class groups, demonstrating that ideal classes inject canonically into Galois cohomology.

Key Points

To establish Galois descent theorems for capitulated affine Bost-Connes boundary systems and characterize how ideal class groups emerge as descent obstructions.
Constructed a capitulated affine system over the Hilbert class field using local field completions and unit-extended scaling monoids.
Applied Hilbert's Theorem 90, the principal ideal theorem, and Green-Julg imprimitivity techniques to analyze equivariant K-theory and descent cocycles.
Proved that the obstruction cocycle represents the class group through a canonical injection into first Galois cohomology, with invariant generators existing strictly when primes are principal.
Demonstrated that Green imprimitivity and Julg's theorem reduce the equivariant K-theory to an inert local model crossed by cyclic groups.
Derived an explicit ladder of unit classes scaling between the local prime class order and the full class number.

Cite This Study

Ruqing Chen (2026) studied this question.

synapsesocial.com/papers/6a9fd75858e84d0ff5b45e4f https://doi.org/10.5281/zenodo.22428735

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Implication

Theoretical analysis uncovers affine descent obstructions in number field class groups, demonstrating that ideal classes inject canonically into Galois cohomology.

Galois descent for affine Bost-Connes boundaries: capitulation, the obstruction cocycle, and the emergence of the class group

Discussion

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Implication

Key Points

Cite This Study

Galois descent for affine Bost-Connes boundaries: capitulation, the obstruction cocycle, and the emergence of the class group

Discussion

Member takes

Implication

Key Points

Cite This Study

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